Target tracking using videos has wide range of applications (see cited references #1-#7), such as, traffic monitoring, video surveillance, security monitoring, etc. Conventional video imagers do not have missing data. In some bandwidth constrained applications, these video imagers may require large bandwidth for transmission, and huge disk space for storage.
A traditional compressive imager is an imager with much fewer pixels than a conventional imager where every pixel is captured. In the traditional compressive sensing approach, a Gaussian random matrix is applied to an image frame with N pixels to obtain one single measurement, and this process is repeated M times for an image. If M<<N, then data compression is achieved. It has been proven that under certain conditions, even if for the case of M<<N, one can still reconstruct the originally image with high fidelity.
In order to accurately perform target classification in compressive measurement domain, it is necessary to know where the target is in an image. If a random Gaussian sensing matrix is applied to the whole raw image, then the spatial information in the raw image is lost, and it is not feasible to perform target tracking and target classification directly in the compressive measurement domain. There are no papers available at present that discuss the above direct tracking and classification problem using Gaussian sensing matrix. However, target tracking, detection, and classification are still hopeful if a random subsampling operator is used to compress the video images. The random subsampling operator is a special case of a random sensing matrix. This is similar to using a sensing matrix by randomly zeroing out certain elements from the diagonal of an identity matrix. FIG. 1 of the present application displays two examples of a random subsampling sensing matrices.
For compressive measurement via a random subsampling operator, a conventional tracking algorithm cannot perform well directly in the compressive measurement domain, even when the compression rate is small (e.g., smaller than 2 or 4 times). FIG. 2 shows one example of a well-known tracker called STAPLE (cited reference #5), which cannot even track the target when the missing rate is at 50%.